1) "Finally, link the libproject to your project."
"your" is unclear, it should say "aerogear-android"
ideally, there would not be compile errors for this project based on the lack of
(Android Tools→ Add Support Library)

2) "Import the project into Eclipse" - this should indicate that an Android import is needed, not a typical Eclipse import

3) Once google-play-services_lib is imported, you need to use
(Android Tools→ Add Support Library) to get it to compile